25 citations · 78 across the 8 of their papers we have counts for
6 papers · 1 filter
Trigonometric Nosé--Hoover oscillator: chaos, periodic orbits and integrability
Wojciech Szumiński, Jaume Llibre
We introduce a trigonometric version of the Nosé-Hoover oscillator in which the quadratic mechanical terms and unbounded thermostat coupling are replaced by bounded trigonometric f…
Dynamics, periodic orbits and non-integrability of the ABC flow
Wojciech Szumiński, Jaume Llibre
We study the Arnold-Beltrami-Childress (ABC) flow in perturbative regimes near its three elementary integrable coordinate axes. Starting from a degenerate family of periodic stream…
Zero-Hopf bifurcation, periodic orbits and non-integrability of the classical Rössler system
Jaume Llibre, Wojciech Szumiński
We investigate the zero-Hopf bifurcation and the local -non-integrability of the original Rössler system. First, we characterize the unique zero-Hopf equilibrium of the syst…
Dynamics and non-integrability of the Swinging Atwood Machine with a massive string: chaos, periodic orbits and resonance structures
Wojciech Szumiński, Jakub Bembenek
Building upon our previous studies on nonlinear variable-length pendulum systems, we investigate the Swinging Atwood Machine with a massive string. In contrast to the classical mod…
Integrability of non-homogeneous Hamiltonian systems with gyroscopic coupling
Wojciech Szumiński, Andrzej J. Maciejewski
We study the integrability of a two-dimensional Hamiltonian system with a gyroscopic term and a non-homogeneous potential composed of two homogeneous components of different degree…
Dynamics and non-integrability of the variable-length double pendulum: exploring chaos and periodicity via the Lyapunov refined maps
Wojciech Szumiński, Tomasz Kapitaniak
This paper extends our previous work~(Szumiński and Maciejewski, 2024), where we explored the dynamics and integrability of the double-spring pendulum. Here, we investigate the var…